Why closed bottle change its weight when I put effervescence tablet? I use several shape, several type of material (glass, metal, plastic), I use two different balances with 0.01g of accuracy. I put oil on gasket, and put upside down (like that I can see if water escape). But always it's the same result, when I put one, two or more effervescence tablets, the weight decrease:
one tablet => -0.03g
two tablets => -0.06g
three tablets => -0.09g
Sure the difference is not big. But if I put an object without effervescence tablet, the weight is always the same (move sometimes +0.01 or -0.01g but never more). The time for decreasing is about 2 minutes so it's not enough for change something from temperature I think especially with glass container.
So, maybe someone has done this experimentation before and know where is my error ? Or maybe someone can test and try this experimentation ?
@Luboš Motl: "Recall that the air density is about 1.3 grams per cubic centimeters", you're sure ? it's not 0.0013 ? 
Yes, I have the same values for glass (2 mm of thickness and one of 3 mm of glass) with a metal cover of 0.8 mm of metal. I done about more than 100 measures. After 2 minutes, the tablet is full dissolved in water and weight move very few after (-0.01g next 2 minutes) but never more.
Maybe I found: when bubbles move up in water, they have gas in it (CO2), this gas move up with a speed, so there is a quantity of movement, the weight losses is the sum of mass of bubbles multiply by speed. Like quantity of movement is conserved, the weight don't change.  
It's possible to use the formula of Newton: force=2mv if top speed is 0.25 m/s the weight losses is 2*0.3/1000*0.25/10 = 0.015 g with 0.3 g of CO2, image show speed that I found on Internet. If it's that, the weight must change with a ball full of air (ping-pong ball) in water. But the CO2 in a tablet is very powerfull, 0.3g give 0.187 liter of CO2, even the ball move faster the volume is not great in a bottle. The ball must be down before close the container. And the gas must relax when the ball reached surface. 
Is it possible it is the rotation of Earth that change the pressure in water due to the centripetal forces ? This give -0.03N for each kg of water.
Good day
 A: Effervescent tablets release $CO_2$, carbon dioxide, into the air when the reaction takes place. For example, sodium-based tablets may contain $NaHCO_3$, the sodium bicarbonate, and it may react with an organic compound – in this case vinegar (acetic acid) like this:
$$ NaHCO_3 + HC_2 H_3O_2 \to H_2 O  + CO_2  + NaC_2 H_3 O_2$$
The water $H_2O$ in the final product is liquid. Only $CO_2$ is the gas that escapes.
If the gas could escape, 0.5 grams of $NaH CO_3$ could release something like 0.25 grams of carbon dioxide – easy to calculate more accurately. Clearly, your measured reduction wasn't this high. This is explained by your bottle's being closed.
However, something did change: the volume of the bottle's interior. Those extra 0.25 grams of $CO_2$ have, at the density 1.8 grams per cubic centimeter, the volume of $0.25/1.8=0.14$ cubic centimeters.
What you measure with the balances isn't just the mass but the total force $mg-\rho_{\rm air}Vg$ (divided by $g$, in the usual units used by scales and balances), acting on the bottle which includes the negative contribution from Archimedes' law (that's why the term is proportional to the volume and the density of the air where the bottle is immersed). With my numbers, the mass of those 0.14 extra cubic centimeters of the air would be 0.18 grams which would be the observed decrease of the weight, still too much. Recall that the air density is about 1.3 grams per cubic centimeters.
In your case, the amount of released $CO_2$ is either smaller; or the bottle is protected against the change of the volume and instead, it keeps the volume almost unchanged and only increases the internal pressure. Whatever the attribution is, the overall numbers in your case happen to be that the weight decreases by 0.03 grams which means that the volume of the bottle increases by $0.3/1.3=0.23$ cubic centimeters and the change of the measured mass is nothing else than the mass of the air you could fit into the added volume of the bottle, because of Archimedes' law.
I have trouble to believe that you get the same results for the metal/glass bottles as you do for the plastic bottles. Their volume changes very badly although the change of the volume may still take place around the cap.
A: Wrong density again... 
Density of CO2 is 1.8 kg/m3 =1.8 gram/liter
Its 100 cc in 1 litre. 
So the density of CO2 is 0.018 gram/cc. 
And for air 0.013 gram/cc. 
Why not recalculate it all? 
